标题： 一种用于H(curl)椭圆半变分不等式的不连续伽辽金方法 显示英文标题

标题： A Discontinuous Galerkin Method for H(curl)-Elliptic Hemivariational Inequalities

摘要： 本文中，我们开发了一种不连续伽辽金（DG）方法来求解H(curl)-椭圆半变分不等式。通过选择适当的数值通量，我们构建了一个内部惩罚不连续伽辽金（IPDG）格式。对IPDG方法进行了全面的数值分析，解决了诸如相容性、有界性、稳定性以及数值解的存在性、唯一性和一致有界性等关键方面。基于这些性质，我们建立了先验误差估计，在适当解正则性假设下证明了数值解的最优收敛阶。最后，给出了一个数值例子，以说明理论预测的收敛阶，并展示所提出方法的有效性。 显示英文摘要

摘要： In this paper, we develop a Discontinuous Galerkin (DG) method for solving H(curl)-elliptic hemivariational inequalities. By selecting an appropriate numerical flux, we construct an Interior Penalty Discontinuous Galerkin (IPDG) scheme. A comprehensive numerical analysis of the IPDG method is conducted, addressing key aspects such as consistency, boundedness, stability, and the existence, uniqueness, uniform boundedness of the numerical solutions. Building on these properties, we establish a priori error estimates, demonstrating the optimal convergence order of the numerical solutions under suitable solution regularity assumptions. Finally, a numerical example is presented to illustrate the theoretically predicted convergence order and to show the effectiveness of the proposed method.